Lectures 21: Routing in Data Networks Eytan Modiano Eytan Modiano
Lectures 21: Routing in Data Networks Eytan Modiano Eytan Modiano Slide 1
Packet Switched Networks Messages broken into Packets that are routed To their destination Packet Network Buffer Packet Switch Eytan Modiano
Packet Switched Networks Packet Network PS PS PS PS PS PS PS Buffer Packet Switch Messages broken into Packets that are routed To their destination Eytan Modiano Slide 2
Routing Must choose routes for various origin destination pairs o/d pairs) or for various sessions Datagram routing: route chosen on a packet by packet basis Using datagram routing is an easy way to split paths Virtual circuit routing: route chosen a session by session basis Static routing: route chosen in a prearranged way based on O/D pairs Eytan Modiano
Routing • Must choose routes for various origin destination pairs (O/D pairs) or for various sessions – Datagram routing: route chosen on a packet by packet basis Using datagram routing is an easy way to split paths – Virtual circuit routing: route chosen a session by session basis – Static routing: route chosen in a prearranged way based on O/D pairs Eytan Modiano Slide 3
Broadcast Routing Route a packet from a source to all nodes in the network Possible solutions Flooding: Each node sends packet on all outgoing links Discard packets received a second time Spanning Tree Routing: Send packet along a tree that includes all of the nodes in the network Eytan Modiano
Broadcast Routing • Route a packet from a source to all nodes in the network • Possible solutions: – Flooding: Each node sends packet on all outgoing links Discard packets received a second time – Spanning Tree Routing: Send packet along a tree that includes all of the nodes in the network Eytan Modiano Slide 4
Graphs A graphG=(N, A) is a finite nonempty set of nodes and a set of node pairs a called arcs or links or edges) N={123} N={1,2,3,4 A={12),(2,3),(1,4,(24)} A={(1,2) Eytan Modiano
Graphs • A graph G = (N,A) is a finite nonempty set of nodes and a set of node pairs A called arcs (or links or edges) 1 2 3 1 2 3 4 N = {1,2,3} N = {1,2,3,4} A = {(1,2),(2,3),(1,4),(2,4)} A = {(1,2)} Eytan Modiano Slide 5
Walks and paths A walk is a sequence of nodes(n1, n2, . nk in which each adjacent node pair is an arc a path is a walk with no repeated nodes Wak(1,2342) Path(1,234) Eytan Modiano
Walks and paths • A walk is a sequence of nodes (n1, n2, ...,nk) in which each adjacent node pair is an arc. • A path is a walk with no repeated nodes. 1 2 4 3 1 2 4 3 Walk (1,2,3,4,2) Path (1,2,3,4) Eytan Modiano Slide 6
Cycles A cycle is a walk(n1, n2, nk) with n1=nk, k>3, and with no repeated nodes except n1= nk cyce(1,2,43,1) Eytan Modiano
Cycles • A cycle is a walk (n1, n2,...,nk) with n1 = nk, k>3, and with no repeated nodes except n1 = nk Cycle (1,2,4,3,1) 1 2 4 3 Eytan Modiano Slide 7
Connected graph a graph is connected if a path exists between each pair of nodes Connected Unconnected An unconnected graph can be separated into two or more connected components. Eytan Modiano
Connected graph • A graph is connected if a path exists between each pair of nodes. 1 2 4 3 1 2 3 Connected Unconnected • An unconnected graph can be separated into two or more connected components. Eytan Modiano Slide 8
Acyclic graphs and trees An acyclic graph is a graph with no cycles A tree is an acyclic connected graph Acyclic, unconnected clic, connected not tree not tree The number of arcs in a tree is always one less than the number of nodes Proof: start with arbitrary node and each time you add an arc you add a node =>N nodes and N-1 links. If you add an arc without adding a node, the arc must go to a node already in the tree and hence form a cycle
Acyclic graphs and trees • An acyclic graph is a graph with no cycles. • A tree is an acyclic connected graph. 1 2 4 3 1 2 3 1 2 3 Acyclic, unconnected Cyclic, connected not tree not tree • The number of arcs in a tree is always one less than the number of nodes – Proof: start with arbitrary node and each time you add an arc you add a node => N nodes and N-1 links. If you add an arc without adding a node, the arc must go to a node already in the tree and hence form a cycle Eytan Modiano Slide 9
Subgraphs G=(N, A)is a subgraph of G=(N, A)if 1)G is a graph 2 Nis a subset of N 3)A is a subset of A One obtains a subgraph by deleting nodes and arcs from a graph Note: arcs adjacent to a deleted node must also be deleted Graph G Subgraph G of G Slide 10
Subgraphs • G' = (N',A') is a subgraph of G = (N,A) if – 1) G' is a graph – 2) N' is a subset of N – 3) A' is a subset of A • One obtains a subgraph by deleting nodes and arcs from a graph – Note: arcs adjacent to a deleted node must also be deleted 1 2 4 3 1 2 3 – Graph G Subgraph G' of G Eytan Modiano Slide 10